1) In addition to the semicolon and colon, you could also use a comma. This is simpler and more common than the semicolon.

There are two types of insects, white
and black.

I prefer commas when there is a dependent clause afterwards.

There are two types of insects, white
and black, on my kitchen table.

2) When using the semicolon, I would expect other commas which would create ambiguity or confusion. However, in this case, it would be the most complicated option, and it is better to avoid it and better to create another sentence instead of an unwieldy one.

With commas:

There are two types of insects, moths,
the white insects, and beetles, the
black insects.

There are two types of insects, moths,
the white insects, and beetles, the
black insects, on my kitchen table.

With semicolons:

There are two types of insects; moths,
the white insects; and beetles, the
black insects.

There are two types of insects; moths,
the white insects; and beetles, the
black insects; on my kitchen table.

In another case, I would use a semicolon for independent clauses:

There are two kinds of insects; the
white insects and the black insects
are on my kitchen table.

From Nishant's example, I would put a comma before the conjunction between "the white insect is white in color" and "the black insect is black in color" because they are two independent clauses:

There are two kinds of insects; the
white insect is white in color, and
the black insect is black in color.

3) The colon is the other useful option besides the comma.

You can use a colon for lists.

There are two types of insects: white
and black.

However, if a dependent clause comes afterwards, it changes the meaning of the sentence.

There are two types of insects: white
and black, on my kitchen table.

This above sentence says that there are only two types of insects in existence, and they all live on "my kitchen table".

If you wanted the same meaning as "There are two types of insects, white and black, on my kitchen table", then you would have to move the dependent clause before the colon.

Recommended:

On my kitchen table, there are two
types of insects: white and black.

Try to keep the colon as close as possible to what it is listing about.

Unrecommended:

There are two types of insects on my
kitchen table: white and black.

Although the above sentence is unrecommended, it is still correct because logically, a list of two items (white and black) will describe the "two types of insects" rather than the one kitchen table.

In many cases, a semi-colon is a tool for joining two clauses that could each be a free-standing sentence; your example illustrates the point nicely as each side of the semi-colon could be a separate sentence. (And, not entirely accidentally, the two halves of my previous sentence, of course, could also each be a free-standing sentence.) They are closely connected, though, and the semi-colon is very useful to indicate that.
–
Jonathan LefflerFeb 21 '11 at 6:02